Southampton, who have always regarded Portsmouth, currently in the fourth tier, as their real rivals, did not drop into the same division as the Cherries until 1953 and from 1960 the pair spent another 50 years apart.
Last season was only the ninth in which the two clubs have played at the same level, which made Bournemouth's joy at winning their top-flight meeting in March all the greater.
A repeat seemed possible once they took the lead early in Sunday's game but Nathan Ake's sixth-minute goal turned out to be one of the few chances they created.
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Having quickly equalised, the visitors took a grip that was never loosened and could have won by one of the biggest margins in the sides' 24 league and cup meetings.
Victory pushed Southampton up to seventh, three points above the Cherries, suggesting they can continue to improve on a poor scoring record this season and match their top-eight finishes of the past three campaigns.
Bournemouth, whose current 10th place is their highest ever, next face a difficult game at league leaders Chelsea on Dec. 26.
For the longer term, they have decided further progress depends on a much larger stadium and,rather than developing the 11,000-capacity Vitality Stadium which they do not own, the club announced earlier this month that they are seeking a new site.
The sort of venue they have in mind will undoubtedly be along the lines of St Mary's, which Southampton moved into in 2001 having left the homely confines of The Dell after 103 years for a modern ground holding more than 32,000.
Bournemouth will go there for the return fixture in April hoping not to have lost much more ground on their neighbours.
(Editing by Ken Ferris)
